Cabbage:In medium sauté pan, sauté cabbage in butter over medium heat until it starts to wilt. Add broth; continue cooking until cabbage is soft. Stir in green onions; cook 1 minute. Remove from heat. (This can be done in advance, stored in refrigerator and reheated when needed.)

Final Preparation:Grill burgers over high heat 8 to 10 minutes, turning once, or until internal temperature is 165° F. Spread both sides of buns with mustard. Place burger on each bun and top with Limburger Cheese. Spoon cabbage over cheese. Place bun top over cabbage.